Differentiation will be used to find whether a function is increasing or decreasing.
Interval and nature of function
Theorem: Let f be continuous on [a, b] and differentiable on (a, b) Then:
- f is increasing in [a, b], if f’ (x) ≥ 0, ∀ x ∈ (a, b)
- f is decreasing in [a, b], if f’ (x) ≤ 0, ∀ x ∈ (a, b)
- f is a constant function in [a, b] if f’ (x) = 0, ∀ x ∈ (a, b)
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